1 SCREEN 12
2 WINDOW (-1, 6)-(17, -20)
3 DEFDBL A-Z
4 FOR x = 0 TO 3 STEP .005
5 y = x ^ (1 / 2)
6 PSET (x, y)
7 NEXT x
8 LINE (-1, 0)-(5, 0)
9 LINE (0, 5)-(0, -5)
10 LINE (1, 5.1962)-(1, -5.1962)
11 LOCATE 1, 20
12 PRINT "Centroid"
13 CIRCLE (3 / 5, 3 / 8), .06
19 LOCATE 10, 1
20 PRINT "The geometrical center of a body is the centroid."
30 PRINT "The centroid is at (<x>,<y>) and the Area is A."
40 PRINT "The distance of the centroid from the x axis is <y>."
50 PRINT "So the moment about the x axis Mx is A<y>."
60 PRINT "The moment about the y axis My is A<x>. A<x>=My, A<y>=Mx"
70 PRINT "Example: Find the centroid of A bounded by y="; CHR$(251); "x, the x axis and the line x=1."
80 PRINT "  "; CHR$(244); "1                  "; CHR$(179); "1"
90 PRINT "A="; CHR$(245); "0 "; CHR$(251); "xdx=(2/3)x^(3/2)"; CHR$(179); "0=2/3"
100 PRINT "   "; CHR$(244); "1               "; CHR$(244); "1                  "; CHR$(179); "1"
110 PRINT "Mx="; CHR$(245); "0 (1/2)("; CHR$(251); "x)^2dx="; CHR$(245); "0 (1/2)xdx=(1/4)x^2"; CHR$(179); "0=1/4"
120 PRINT "   "; CHR$(244); "1         "; CHR$(244); "1                       "; CHR$(179); "1"
130 PRINT "My="; CHR$(245); "0 x"; CHR$(251); "xdx = "; CHR$(245); "0 x^(3/2)dx=(2/5)x^(5/2)"; CHR$(179); "0=2/5"
140 PRINT "<x>=My/A=(2/5)(3/2)=3/5"
150 PRINT "<y>=Mx/A=(1/4)(3/2)=3/8"
160 PRINT "So the centroid is at (3/5,3/8)"
170 SYSTEM